To answer the problems of interaction between attributes, we propose to take inspiration from the work of [1]}. The prediction task is a framework close to the situation called "coalitions", where groups of attributes can influence the prediction of the model. In this context, each attribute cannot be considered as independent, but in all possible attributes combinations. The influence of an attribute is measured according to its importance in each coalition. We can then refer to the coalition games as defined by Shapley in [2]}: A coalitional game of \(N\)  players is defined as a function mapping subsets of players to gains \(g: 2^{N} \mapsto \mathbb {R}\) . The parallel can easily be drawn with our situation, where we wish to assess the influence of a given attribute in every possible coalition of attributes. We then look at not only the influence of the attribute but also its use in all subsets of attributes. We thus define the complete influence of an attribute \(a_{i} \in A\)  on the classification of an instance \(x\)  : given a dataset of instances described along the attributes of \(A\) , the complete influence of the attribute \(a_{i}\)  on the classification of an instance \(x\)  by the classifier confidence function \(f\)  on the class \(C\)  is dependant on the influence of all the possibles subgroups \(A^{\prime } \subseteq A\)  which does not contain \(a_i\) . Thus, the complete influence of \(a_i\)  is :
\(\mathcal {I}^{C}_{a_{i}}(x) = \sum _{A^{\prime } \subseteq A \backslash a_{i}} p(A^{\prime },A)*(inf^{C}_{f,({A^{\prime }\cup a_{i}})}(x) - inf^{C}_{f,A^{\prime }}(x))\) 
